I think it should be C(13,6)C(4,1)C(13,6)C(3,1)C(26,1), since the second suit must be different from the first. Other than that, it looks fine to me.
I think your tutors answer doesn't require the suits form the sextuples to be different, and it doens't require the extra card to be form a different suit than the sextuples. However, than the correct answer is:
$$C(13,12)C(4,1)C(39,1)+ C(13,13)C(4,1)+ C(4,1)C(13,6)C(3,1)C(13,6)C(26,1)+ C(4,1)C(13,7)C(3,1)C(13,6)$$
So you should ask your tutor about the exact conditions for this problem.